分数算子的Charef有理逼近与新颖标度方程的奇异性质

Charef rational approximation of fractional operators and singular properties of novel scale equations

根据分数算子的Charef有理逼近的单分数幂极点、零点模型,引入两类新型非正则标度方程——新颖标度方程,该方程用于表征分数算子的Charef有理逼近的极限情形,并具有物理可实现性.首先考察新颖标度方程有理函数序列的运算有效性、运算性能,对比与典型标度方程之间的差异.发现新颖标度方程有理函数序列的真实解与近似解结果不同,该方程为标度方程的近似求解法提供了新的思路.之后结合零极点子系统的运算局域化特征,定量分析新颖标度方程的运算振荡周期.最后,发现复平面内的零极点分布规律与典型标度方程不同,找出新颖标度方程的奇异特性.

According to the single-fraction power pole and zero model of the Charef rational approximation of the fraction operator,two new types of non-normal scaling equations-the novel scaling equation are introduced,which are used to characterize the limit cases of the Charef rational approximation of the fraction operator.It is physically realizable.Firstly,we investigate the operational validity and performance of the rational function sequence of the novel scale equation,and compare the difference with the typical scale equation.It is found that the real solution of the rational function sequence of the novel scale equation is different from the approximate solution.This equation provides a new idea for the approximate solution of the scale equation.Then combined with the localization feature of the zero-pole subsystem,the operation oscillation period of the novel scaling equation is quantitatively analyzed.Finally,it is found that the distribution of poles and zeros in the complex plane is different from the typical scaling equation,and the singular characteristics of the novel scaling equation are found.